The probability distribution of random variable X is given by: X 1 2 3 4 5 P ( X ) K 2 K 2 K 3 K K Let p = P ( 1 < X < 4 ∣ X < 3 ) . If 5 p = λ K , then λ is equal to

Step-by-step solution

Σ P ( X ) = 1 ⇒ K + 2 K + 2 K + 3 K + K = 1 K = 1 9 P = P ( 1 < X < 4 ∣ X < 3 ) = P ( X = 2 ) P ( X < 3 ) P = 2 K 9 K K 9 K + 2 k 9 K = 2 3 5 P = λ K 5 × 2 3 = λ × 1 9 ⇒ λ = 30